Smithsonian has some of the collection (heck, I get to see Kermie every month... still wondering who *one* of the muppets in the front row of the picture with it is though). They had more on display at the American History museum before the renovation was started, including most of two costumes/puppets from The Dark Crystal... they weren't looking so great at the time, and you *know* that reasonable conservation work is done before things go on display, even if it can't be done always.

Don't know how much was offered the museum, though I do know that not *quite* everything offered the museums gets accepted.

Disney has some of it as well.